Submission: 2014, Jan 8
In the present article we investigate properties of the category of the integral Grothendieck-Chow motives over a field. We discuss the Krull-Schmidt principle for integral motives, provide a complete list of the generalized Severi-Brauer varieties with indecomposable integral motive, and exploit a relation between the category of motives of twisted flag varieties and integral p-adic representations of finite groups.
2010 Mathematics Subject Classification: 14C15, 14M15, 20G15
Keywords and Phrases: Linear algebraic groups, twisted flag varieties, generalized Severi-Brauer varieties, Chow groups and motives, Maranda theorem.
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